This work is concerned with a system of nonlinear wave equations with nonlinear damping and source terms acting on both equations. We prove a global nonexistence theorem for certain solutions with positive initial energy.

We prove existence and uniqueness of global classical solutions to the generalized large-scale semigeostrophic equations with periodic boundary conditions. This family of Hamiltonian balance models for rapidly rotating shallow water includes the L model derived by R. Salmon in 1985 and its 2006...

Blow up of solutions to systems of nonlinear wave equations with degenerate damping and source terms supplemented with the initial and Dirichlet boundary conditions is shown in [13], in a bounded domain O ? Rn, where n = 1,2,3 and the initial energy is negative. Our result extends this previous...

We study the initial-boundary value problem for a system of nonlinear wave equations with nonlinear damping and source terms, in a bounded domain. The decay estimates of the energy function are established by using Nakao's inequality. The nonexistence of global solutions is discussed under some...

The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray-Schauder fixed point theorem to...

This paper deals with regularity and stability of solutions to an initial-boundary value problem of a semilinear wave equation. This equation admits space-time dependent coefficients and a memory boundarylike antiperiodic condition. For regularity or existence of a unique strong solution, the...

The initial-boundary value problem for a class of nonlinear wave equations system in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set and obtain the asymptotic stability of global solutions through the use of a difference...

In this paper, we discuss the nonlinear wave equations with nonlinear damping and source terms. By using the potential well methods, we get a result for the global existence and blow-up of the solutions.

This paper establishes the global existence of classical solution to the system of homogeneous, isotropic hyperelasticity with time-independent external force, provided that the nonlinear term obeys a type of null condition. The authors first prove the existence and uniqueness of the stationary...